Simulations of multiple-body interactions (often called “N-body” problems) are useful in a number of problem areas including celestial dynamics and computational chemistry. Bio-molecular or electrostatic particle interaction simulations complement experiments by providing a uniquely detailed picture of the interaction between particles in a system. An important issue in simulations is the simulation speed.
Determining the interaction between all pairs of bodies in the system by enumerating the pairs can be computationally intensive, and thus, alternate interaction schemes are often used. For example, all particles within a predefined radius of a particular particle interact with that particle while particles farther away are ignored.
In some simulation schemes an Ewald method is used, which can reduce the amount of computation as opposed to enumeration of all potentially interacting pairs of bodies. For simulation of electrostatic systems, the Ewald method divides the electrostatic potential defined as a function of location into two main terms. A “screening” charge distribution, typically chosen to be Gaussian, is (notionally) centered on every point charge. This screening charge distribution is chosen to give the same charge magnitude but with an opposite sign as the point charge on which it is centered. The electrostatic potential due to the combination of the point charge and the screening charge falls off rapidly with distance. Thus, this first contribution to the electrostatic potential can be neglected beyond a relatively small cut-off distance. The second contribution to the electrostatic potential is due to the negative effect of the contribution of all the screening charge distributions alone, essentially compensating for their introduction in the first term. This second contribution can be obtained by solving the Poisson equation for the charge distribution given by the sum of screening charge distributions.